<P style="MARGIN: 0in 0in 0pt 0.5in" class=MsoNormal><SPAN style="FONT-FAMILY: 'Calibri', sans-serif; FONT-SIZE: 12pt; mso-bidi-font-size: 9.0pt"><FONT color=#000000>Important points in 7.5.4:<BR style="mso-special-character: line-break"><BR style="mso-special-character: line-break"><?xml:namespace prefix = o /><o:p></o:p></FONT></SPAN></P>
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<LI style="MARGIN: 0in 0in 0pt; mso-list: l0 level2 lfo1; tab-stops: list 1.0in" class=MsoNormal><SPAN style="FONT-FAMILY: 'Calibri', sans-serif; FONT-SIZE: 12pt; mso-bidi-font-size: 9.0pt"><FONT color=#000000>Understanding Discrete vs. Continuous<BR style="mso-special-character: line-break"><BR style="mso-special-character: line-break"><o:p></o:p></FONT></SPAN></LI>
<LI style="MARGIN: 0in 0in 0pt; mso-list: l0 level2 lfo1; tab-stops: list 1.0in" class=MsoNormal><SPAN style="FONT-FAMILY: 'Calibri', sans-serif; FONT-SIZE: 12pt; mso-bidi-font-size: 9.0pt"><FONT color=#000000>For a Continuous Random Variable, probabilities of an interval of values are represented by areas (that are sectioned off by vertical slices).<BR style="mso-special-character: line-break"><BR style="mso-special-character: line-break"><o:p></o:p></FONT></SPAN></LI>
<LI style="MARGIN: 0in 0in 0pt; mso-list: l0 level2 lfo1; tab-stops: list 1.0in" class=MsoNormal><SPAN style="FONT-FAMILY: 'Calibri', sans-serif; FONT-SIZE: 12pt; mso-bidi-font-size: 9.0pt"><FONT color=#000000>For a Continuous Random Variable the probability that X=(<I style="mso-bidi-font-style: normal">any specific value</I>) = 0.<SPAN style="mso-spacerun: yes">&nbsp; </SPAN>For a continuous variable there are an infinite number of possible values the variable can have.<SPAN style="mso-spacerun: yes">&nbsp; </SPAN>Even if you think of each one as equally likely (as in a Uniform Distribution), the probability of any one particular value is 1/(infinity) which is 0.<BR style="mso-special-character: line-break"><BR style="mso-special-character: line-break"><o:p></o:p></FONT></SPAN></LI>
<LI style="MARGIN: 0in 0in 0pt; mso-list: l0 level2 lfo1; tab-stops: list 1.0in" class=MsoNormal><SPAN style="FONT-FAMILY: 'Calibri', sans-serif; FONT-SIZE: 12pt; mso-bidi-font-size: 9.0pt"><FONT color=#000000>"<B style="mso-bidi-font-weight: normal"><I style="mso-bidi-font-style: normal">expected value</I></B>" is a term that means the mean (average)<BR style="mso-special-character: line-break"><BR style="mso-special-character: line-break"><o:p></o:p></FONT></SPAN></LI>
<LI style="MARGIN: 0in 0in 0pt; mso-list: l0 level2 lfo1; tab-stops: list 1.0in" class=MsoNormal><SPAN style="FONT-FAMILY: 'Calibri', sans-serif; FONT-SIZE: 12pt; mso-bidi-font-size: 9.0pt"><FONT color=#000000>the mean (“expected value”) is the "balance point" of the area<BR style="mso-special-character: line-break"><BR style="mso-special-character: line-break"><o:p></o:p></FONT></SPAN></LI></UL></UL>
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